Congrats, sounds like quite a big plot Axel2801!
Those two weeds are pretty hardcore so you have 3 options;
The hard way: dig it all out.
The easier way: look at 'no-dig' which involves smothering the weeds rather than digging out.
The non-organic way: spray with chemicals.
It depends on how long you're giving yourself, how fit you are and how easily you can source things like compost (for no-dig). Personally I'd do the digging out but a plot that size and the current weather conditions may mean you only free say half of it up for growing by next March. There are a lot of forumites here who use the no-dig method who may be able to advise on that front. The spraying way might not be feasible at this time of year when it's so wet but again, I'm no expert here.
Whatever you decide, good luck and check in here for advice and tips!